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Distributed Adaptive Fault-Tolerant Control of Uncertain Multi-Agent Systems
Mohsen Khalili, Xiaodong Zhang, Marios M. Polycarpou, Thomas Parisini, Yongcan Cao
TL;DR
Reliable leader-following consensus in uncertain nonlinear multi-agent systems is difficult when individual agents can develop faults. The paper proposes distributed adaptive FTC using local diagnosis and staged controller reconfiguration, and establishes stability and consensus under the stated assumptions across fault-handling modes.
Problem
The paper addresses distributed fault-tolerant leader-following consensus for uncertain nonlinear multi-agent systems when faults may occur in individual agents.
Method
Each agent uses local measurements and neighbor information with adaptive fault estimators and a controller that reconfigures after fault detection and isolation.
Results
The paper establishes closed-loop stability and leader-following consensus under stated assumptions across baseline, fault-detection, and fault-isolation modes.
Takeaways & Limitations
The proposed distributed FTC scheme supports leader-following consensus despite faults within the considered uncertain-system class and assumptions.
Takeaways & Limitations
The analysis assumes bounded modeling uncertainty and a fixed connected undirected intercommunication topology, while more general system structures remain future work.
Abstract
from arXiv · showhide
This paper presents an adaptive fault-tolerant control (FTC) scheme for a class of nonlinear uncertain multi-agent systems. A local FTC scheme is designed for each agent using local measurements and suitable information exchanged between neighboring agents. Each local FTC scheme consists of a fault diagnosis module and a reconfigurable controller module comprised of a baseline controller and two adaptive fault-tolerant controllers activated after fault detection and after fault isolation, respectively. Under certain assumptions, the closed-loop system's stability and leader-follower consensus properties are rigorously established under different modes of the FTC system, including the time-period before possible fault detection, between fault detection and possible isolation, and after fault isolation.
1. INTRODUCTION
The paper addresses reliable operation of distributed multi-agent systems despite agent faults by developing a distributed adaptive fault-tolerant control methodology. Each agent uses local measurements and neighbor information for diagnosis and reconfigurable control.
- Distributed multi-agent systems require fault diagnosis and accommodation to maintain reliable and safe operation when some agents behave faultily.
- Centralized fault-diagnosis methods may be unsuitable for large-scale distributed systems because they require global models, real-time sensor access, and substantial computational and communication resources.
- The proposed methodology assigns each agent a local FTC scheme using local measurements and information exchanged between neighboring agents.
- Each local scheme combines nonlinear adaptive fault estimators with a reconfigurable controller containing baseline, post-detection, and post-isolation controllers.
- Under stated assumptions, the paper establishes closed-loop stability and leader-following consensus for the baseline and adaptive fault-tolerant controllers.
2. GRAPH THEORY NOTATION
The section defines directed and undirected communication graphs, their neighbor and adjacency representations, and the Laplacian matrix used to describe information exchange among agents.
- A directed graph consists of nodes and ordered edges, where an edge identifies the receiving child node and sending parent node.
- A directed graph contains a directed spanning tree when one root node has directed paths to every other node.
- The neighbor set contains nodes with directed edges into a given node, while the weighted adjacency matrix records positive communication weights on those edges.
- The Laplacian matrix uses weighted neighbor sums on its diagonal and negative edge weights off diagonal; for undirected graphs, both adjacency and Laplacian matrices are symmetric.
3. PROBLEM FORMULATION
The paper formulates distributed leader-following FTC for uncertain nonlinear agents with modeled fault classes, local diagnostic information, and controller reconfiguration across detection and isolation stages.
- Each agent model includes known nonlinearities, modeling uncertainty, and a nonlinear fault term whose step profile activates at an unknown fault time.
- The model generalizes single-integrator multi-agent dynamics by explicitly including fault functions and modeling uncertainty for fault-tolerance and robustness analysis.
- Each agent may have a finite set of possible nonlinear fault functions, with fault parameters belonging to known compact sets.
- The objective is robust distributed fault-tolerant leader-following consensus for uncertain multi-agent systems using diagnostic information.
- The uncertainty is assumed bounded, and a fixed connected undirected communication graph is required so agents can distinguish faults from uncertainty and exchange sufficient information.
- The controller switches from baseline operation to detection-stage accommodation at Td and to isolation-stage accommodation at Tisol.
- After fault detection, the controller compensates for an unknown fault to preserve bounded signals and some consensus performance; after isolation, it uses the identified fault type to improve performance.
4. BASELINE CONTROLLER DESIGN
The baseline controller uses neighbor and leader information to handle modeling uncertainty before faults, and the analysis establishes asymptotic leader-following consensus under the graph assumptions.
- The baseline controller is designed for agents to track a time-varying leader despite possible plant modeling uncertainty.
- The leader is treated as agent M + 1, yielding a topology with the leader as the root of a spanning tree.
- The directed communication topology is analyzed using an auxiliary Laplacian associated with an undirected leader graph, while the actual leader sends data without receiving it.
- Theorem 1 states that, without faults, the baseline controller achieves asymptotic leader-follower consensus with the time-varying reference state.
- The Lyapunov analysis uses collective agent states and a symmetrized Laplacian structure to establish a nonpositive derivative under the uncertainty bound.
- Consensus follows because the Lyapunov derivative is negative definite with respect to relative states, with zero derivative only when the collective states agree.
5. DISTRIBUTED FAULT DIAGNOSIS
The distributed fault-diagnosis architecture assigns each agent a local detection and isolation component using local measurements and communicated neighbor information. Adaptive estimators generate bounded state errors for fault detection and distinguish among fault types before controller reconfiguration.
- Architecture: Each agent has a local FDI component with one fault detection estimator and a bank of nonlinear adaptive fault isolation estimators.The isolation estimators correspond to the different nonlinear fault types associated with that agent.
- Fault detection: The distributed fault detection estimator uses local state and input variables together with communicated information from neighboring agents.Its observer gain is chosen through a positive definite matrix.
- Fault detection: Before fault occurrence, modeling uncertainty produces nonzero estimation error, for which componentwise bounds are derived and used to construct detection thresholds.The threshold integral can be implemented as the output of a linear filter driven by a bound on the modeling uncertainty.
- Fault detection: A fault is detected when at least one component of the local state-estimation error exceeds its corresponding threshold.The detection time is defined as the first such threshold crossing after fault occurrence.
- Fault isolation: After detection, nonlinear adaptive isolation estimators are activated, with fault-parameter estimates constrained through projection-based adaptation.Each estimator produces error bounds and threshold functions used to exclude incompatible fault types.
- Fault isolation: Fault type s is isolated when every competing estimator exceeds its threshold in at least one error component at some finite time.The decision rule concludes that fault s occurred only after all alternative fault types have been excluded.
6. FAULT-TOLERANT CONTROLLER MODULE
The fault-tolerant controller reconfigures after detection and isolation, using adaptive approximation before isolation and fault-parameter adaptation after isolation. Under the stated assumptions, these controllers preserve boundedness, stability, and asymptotic leader-follower consensus.
- Accommodation before Fault Isolation: After fault detection, adaptive approximators estimate the unknown process fault while the controller is reconfigured before fault isolation.The design uses neural-network models because the fault type and fault function are unavailable before isolation.
- Accommodation before Fault Isolation: The process-fault model represents the unknown fault as an adaptive estimate plus a neural-network approximation error.The approximation error is defined as f_ip(x_i) − ˆf_ip(x_i,ϑ_ip), with assumptions imposing a known bounding function.
- Accommodation before Fault Isolation: The Lyapunov-based adaptive design establishes bounded signals and parameter estimates during the interval between fault detection and isolation.The analysis uses a Lyapunov function containing consensus-state, neural-network parameter, and bounding-parameter estimation errors.
- Accommodation before Fault Isolation: Leader-follower consensus is achieved asymptotically after detection, including during the period before fault isolation.The result states x_i − x_r → 0 as t → ∞ for a time-varying reference state.
- Accommodation after Fault Isolation: After fault isolation, adaptive fault-tolerant controllers estimate the isolated fault parameter using a projection operator and positive-definite learning-rate matrices.The process-fault and actuator-fault cases each have a corresponding adaptive controller and parameter update law.
- Accommodation after Fault Isolation: The post-isolation adaptive laws yield a nonpositive Lyapunov derivative and guarantee asymptotic leader-follower consensus with a time-varying reference.The proofs use ˙V_p ≤ −x_p^T L̄ x_p and conclude x_i − x_r → 0 as t → ∞.
7. SIMULATION RESULTS
The simulation evaluates the distributed FTC method on five uncertain ground-vehicle agents tracking a time-varying leader under a process fault in agent 1. The fault is detected and isolated promptly, and adaptive FTC preserves leader-following consensus that fails without FTC.
- Simulation setup: The simulation considers a networked multi-agent system of 5 agents with unicycle-like ground-vehicle dynamics and a time-varying leader.Each agent uses orientation and linear velocity inputs, while the leader position is time varying.
- Fault diagnosis: The fault-detection residual for agent 1 exceeds its threshold immediately after fault occurrence, enabling timely detection.The detection residual and threshold are generated by the local fault detection estimator.
- Fault diagnosis: The first fault-isolation residual remains below threshold while the second exceeds it immediately, identifying fault type 1.The same qualitative diagnosis behavior is reported for the second state, although its plots are omitted.
- Control performance: Leader-following consensus is achieved with the proposed adaptive fault-tolerant controllers, whereas the agents cannot follow the leader without FTC controllers.After isolation, the controller uses an adaptive gain of Γ_i = 0.2; before isolation, an RBF network approximates the process fault.
8. CONCLUSION
The paper develops distributed adaptive FTC for uncertain multi-agent systems and establishes leader-following consensus under faults. It also identifies extensions to systems with more general structure as future research.
- Conclusion: Under certain assumptions, adaptive FTC controllers achieve leader-following consensus for a class of uncertain multi-agent systems in the presence of faults.The conclusion states the result at the level of the distributed FTC problem addressed by the paper.
- Future work: Extending the approach to systems with more general structure remains an identified topic for future research.The conclusion explicitly marks this extension as future work.